The present invention relates to a method of and an apparatus for measuring an energy gap of a semiconductor material by using an image processing system.
A dimension of an energy gap serving as the most important electrical characteristic coefficient of a semiconductor material has been heretofore induced by using a spectrophotometer which continuously varies a wavelength of a light source and irradiates the light produced from the lightsource to a semiconductor sample so as to obtain an optical transimission spectrum on the basis of a theory which will be described later.
Such a spectrophotometer is known as the most important means for measuring a band structure of a semiconductor material.
Generally, when photons having an energy level `h.sub..nu. ` approximate to an energy gap Eg are irradiated to the semiconductor material, electrons are released from a conduction band to a valence band and, at this time, photons are absorbed in such a way of a light absorptive mechanism known so called as a fundamental absorption.
As noted above, from the photon induced electronic transition between bands of the material, the energy gap Eg of the semiconductor material can be easily measured.
The optical transmission in the semiconductor material can be expressed by a Dubrowskii formulation defined as belows. That is: EQU e.sup.-(.alpha.d) =[(A.sup.2 +2TA).sup.2 +4T.sup.2 ].sup.1/2 -(A.sup.2 +2TA)/2T (1)
where, .alpha. denotes an absorption coefficient, d denotes a thickness of a semiconductor sample and R denotes the amount of reflected light; and A+T+R=1.
When the optical absorption is relatively large, the equation (1) can be expressed as the following MOSS equation. That is: EQU T=(1-R).sup.2 exp.sup.-(.alpha.d) ( 2)
Also, the absorption coefficient .alpha. in a fundamental absorption edge (band to band transition) can be expressed as the following equations with respect to a direct transition or indirect transition.
In the case of the direct transition as shown in FIG. 1(a) ##EQU1## in the case of the indirect transition as shown in FIG. 1(b) ##EQU2## where, Egd denotes a direct energy gap, Egi denotes an indirect energy gap and E.sub..theta. denotes a phonon energy gap. In the equations (4) the first term means that the phonons are emitted while the second term means that the phonons are absorbed. Accordingly, from the equations (3) and (4), the direct and indirect energy gaps Egd and Egi are induced by drawing tile relation of .alpha..sup.2 =f(h.sub..nu.) and .alpha..sup.1/2 =f f(h.sub..nu.) on respective graphs (a) and (b) as shown in FIG. 1. The value a is obtained from the transmitted light T and reflected light R under the given thickness of the semiconductor sample using the equation (1) or (2). PA1 analyzing character of a reference semiconductor sample and setting an energy gap pixel value; PA1 estimating a transfer function between the pixel value comprising a transmission spectrum image and wavelengths of the corresponding pixels, positioning the sample properly and then obtaining a live image; PA1 storing the live image and scanning the respective pixel values along a x-axis of the image; PA1 sequentially comparing the respective pixel value and the energy gap pixel value, reading a x-coordinate of the pixel having a value coinciding with each other as the comparison value, and converting the wavelength of the pixel into a unit of eV to estimate the energy gap Eg. PA1 a computer for executing all operation and control functions associated with measurement of the energy gap; PA1 a lens for focusing the lighting beam irradiated from a light source; PA1 a polychromator for irradiating the spectrum of the light to the sample; PA1 optical filters for converting the polychromator's spectrum band into corresponding wavelength values. PA1 an image acquisition apparatus for storing the image displayed on the monitor into memory PA1 an image signal processor for manipulating the digital data; and PA1 an energy gap detecting and displaying apparatus for defining a functional relation between the coordinate value and wavelength of the pixel.
In the case of the direct transition of the equation (3), because the value .alpha. is set to zero under tile photon energy below the energy gap Eg, the transmission spectrum of a semiconductor material with no impurity is present arid the energy gap is shown in FIG. 2. From the spectrum shown in FIG. 2, the direct energy gap Egd can be obtained. That is, a start point of transmission in FIG. 2 indicates the energy gap Eg.
The method can be applied to most of compound semiconductor compounds because they have generally speaking the direct energy gap characteristics.
A goal underlying the present invention is to achieve a direct measurement of the energy gap with an infrared imaging system.
Accordingly, object of the present invention is to provide a method of and an apparatus for measuring an energy gap of semiconductor, in which a light source of a given band is irradiated to a semiconductor sample, and an image response is displayed on a monitor by applying a digital processing algorithm to obtain the images on the monitor.
To achieve the above object, according to one embodiment, the present invention contemplates a method of measuring an energy gap of a semiconductor, comprising:
According to another aspect, the present invention provides an apparatus for measuring an energy gap of a semiconductor, comprising:
With the present invention thus constructed, the light source of a given bandwidth is irradiated on the semiconductor sample and the response is imaged by the digital image processing system. Accordingly, the energy gap can be directly measured from the image displayed on the image processing system.
The above and other objects and advantages will be understood from the following description taken with reference to the accompanying drawings.